Ion diffusion retarded by diverging chemical susceptibility

For first-order phase transitions, the second derivatives of Gibbs free energy (specific heat and compressibility) diverge at the transition point, resulting in an effect known as super-elasticity along the pressure axis, or super-thermicity along the temperature axis. Here we report a chemical analogy of these singularity effects along the atomic doping axis, where the second derivative of Gibbs free energy (chemical susceptibility) diverges at the transition point, leading to an anomalously high energy barrier for dopant diffusion in co-existing phases, an effect we coin as super-susceptibility. The effect is realized in hydrogen diffusion in vanadium dioxide (VO2) with a metal-insulator transition (MIT). We show that hydrogen faces three times higher energy barrier and over one order of magnitude lower diffusivity when it diffuses across a metal-insulator domain wall in VO2. The additional energy barrier is attributed to a volumetric energy penalty that the diffusers need to pay for the reduction of latent heat. The super-susceptibility and resultant retarded atomic diffusion are expected to exist universally in all phase transformations where the transformation temperature is coupled to chemical composition, and inspires new ways to engineer dopant diffusion in phase-coexisting material systems.

The present manuscript reports anomalously high energy barrier for dopant diffusion in coexisting phases across the metal to insulator transition point of VO2, and attributed this behavior to the volumetric energy penalty that the diffusers need to pay for the reduction of latent heat.In general, the manuscript is well written and the conclusion is rather interesting.Nevertheless, I have the following suggestions for further improvements.
1)Figure 1c, how the error bar was determined when calculating D?
2)Also for Figure 1c, another thing is that it seems that D is smaller at the insulating phase region approaching to the critical temperature but the D-T tendency seems smooth in the region associated with the metallic phase approaching to the critical temperature.I was wondering how the critical temperature (TMIT) should be determined, since it is hard to tell whether the metallic and insulating phase 'should' co-exist in across TMIT or just at the temperature region slightly below TMIT?This needs to be further clarified.
3)The experiments as demonstrated in Figure 2 was well designed, and in the present case the hydrogenation seems to reduce the resistivity of VO2 that stabilizes the metallic phase.
Nevertheless, the hydrogenation of VO2 can also trigger an insulating state under mild hydrogenation temperatures and high hydrogen concentration (e.g., Nat. Mater.2016, 15, 1113, or J. Phys. Chem. Lett. 2022,13,8078), in which situation higher amount of hydrogen will be incorporated within the material.I was wondering whether the mixing phase adjacent to the metal to insulator transition temperature will affect D in this case.
4)It seems that the less effective hydrogen diffusion within the mixing phase region was caused by the additional energy as caused by the metallicity of VO2 via hydrogenation.
Nevertheless, I doubt whether such energy should be considered to be analogous to the latent heat as released when varying temperature across TMIT.Of course this may be correct, but I suggest to be more careful in making a universal conclusion from that perspective.1c should be also demonstrated for W doped VO2, in which situation the magnitude of TMIT is reduced via substituting V by transition metal with higher valance.Whether this can shift the dash line as shown in Figure 1c leftwards will to some extent testify the universality of the present conclusion.6)One confirming experiment worthy to be consider in the future (not necessarily to be done now for this work) is associated with the hydrogen diffusion within rare-earth nickelates.From the one side the latent heat across TMIT is much smaller compared to VO2, while the hydrogenation triggered reduction in G should be comparable.From the other side, the resistivity of rare-earth nickelates elevate abruptly, the tendency of which is just the opposite compared to the present one.This will be a perfect supplementary experiment to the present work.

Reviewer #2 (Remarks to the Author):
In this work, the authors provided the effect of second derivative of Gibbs free energy on hydrogen diffusion in VO2.It reported hydrogen faced three times higher energy barrier and over one order of magnitude lower diffusivity when crossing a metal-insulator domain wall in VO2.Furthermore, they employed the first-principles calculations to reveal the hydrogen diffusion along various axes.However, after a comprehensive evaluation of this work, I think it can't provide profound scientific meaning, also can't attract broad attention.1) As shown in Formula (1), it seems that the Gibbs free energy is linear with the hydrogen atomic fraction (x).However, the doping of hydrogen in VO2 could induce a metallic or insulator state depending on the concentration of hydrogen (Nat. Mater.15, 1113, 2016).
Obviously, the provided module can't illustrate the effect of high concentration hydrogen on VO2.
2) The diffusion energy barriers of hydrogen along various axes of VO2 were calculated, while the specific diffusion routes should be present in Fig. 3.

Reviewer #3 (Remarks to the Author):
In the present manuscript, one chemical analogy was proposed to display the singularity of the second derivatives of Gibbs free energy across first-order phase transitions, leading to an anomalously high energy barrier for dopant diffusion in co-existing phases within the hydrogenated VO2 single crystal microbeams and polycrystalline films.This work also applied the chemical susceptibility to analyze other co-existing phase systems.In general the manuscript is interesting but the following concerns must to be addressed: 1) The author attempts to introduce the contribution of hydrogen occupancy in the driving force of phase transition and explains the singularity caused by this term.In the first paragraph of page 9 of the manuscript, the author points out: "…leads to a chemical energy penalty of |Δγ| for a hydrogen ion to diffuse from an M-domain into an I-domain.This effect is very similar to the mechanical energy penalty of |σMITΔε|…".However, the chemical energy dependency caused by hydrogen might be essentially considered as the stress effect itself.For materials with phase transition, the local chemical stress caused by doping often exhibits the same effect as macroscopic stress, such as biaxial stress caused by the substrate in nickelates(Matter, 2020, 2, 1) and isotopic doping effects in conductive polymers (J. Chem. Soc., Perkin Transaction2, 1995).In Table .S3, it can be seen that the lattice expansion of the hydrogenated rutile phase and intrinsic rutile phase reaches 4%.Therefore, it is suggested that the author increase the discussion on local chemical pressure to exclude the influence of other factors on the analogy of chemical magnetization.
2) Fig. S7 is not mentioned in the main text.The accompanying issue is that this article lacks a sufficient explanation of the structural information, morphology, and orientation of synthesized microbeams in the main manuscript.
3) Fig. 2(b) lacks of detailed legend to distinguish between hollow triangles and solid circles.
4) The ex-situ observation of Raman spectra and fitting of diffusion coefficients for hydrogen-induced MIT may overlook some potential factors, such as the chemical gradient introduced by the non-uniform distribution of hydrogen atoms along the microbeams.The influence of this part on the hydrogen diffusion coefficient is usually not significant.But when more hydrogen atoms are pinned onto the domain wall (due to the diffusion barriers, in the author's context), the blocking effect of this part of the chemical gradient is not considered.I suggest the author to further discuss to clarify the effects of enthalpy and formation energy.5) In XPS analysis, the integrated area of the peak may be more convincing than the peak intensity.This can be achieved through more detailed peak fitting.
6) Lack of discussion on the difference in hydrogen diffusion rates between pristine tungsten-doped samples and pristine VO2 samples.The effect of tungsten dopant on hydrogen diffusion may affect the independence of domain wall analysis.
7) The analysis of Fig. 1(d) appears in multiple places in the text, which is relatively scattered and not conducive to the coherence of the discourse.The relevant paragraphs on page 7 can be integrated with those on page 9. 8) From a microscopic perspective, will hydrogen atoms continuously cross the M-I domain wall barrier during diffusion?This may be related to whether hydrogen is the sole driving force behind the M-I transition when T<TMIT.The lattice expansion caused by electron doping may drive the local transformation of other I-phases.Therefore, hydrogen may be discontinuous across domain walls.The exploration of this mechanism may require deeper calculations and more powerful characterization techniques in the future.9) I am curious about the result of simultaneous hydrogenation on both sides of a finite beam.For a sufficiently uniform microbeam, hydrogen is expected to symmetrically promote the formation of the M-phase under the same conditions.When the domain walls on both sides are very close, the phase transition behavior of the central I phase may become anomalous.When any hydrogen atom overcomes a chemical barrier, it will cause a sudden collapse of the domain wall on one side of the phase.This may trigger novel physical phenomena.In future work, the author can continue to explore in depth.10) Concerning the hydrogen interaction with correlated or phase transition materials, other systems than VO2 should be also mentioned, and whether analogous effects are expected should be also discussed (e.g., Nat commun 2019, 10, 694;Adv Mater 2020, 1905060) Reviewer #4 (Remarks to the Author): The authors introduced chemical susceptibility as a thermodynamic parameter to show that it diverges near a first-order phase transition.They used hydrogen-doped vanadium dioxide (VO2) as a model system and based their findings on their experimental work on VO2 nanobeams hydrogenated via spill-over.The manuscript brings a new perspective to hydrogen doping and its effects on VO2.Moreover, the findings reported in the manuscript have the potential to impact related research fields.However, I think further clarification on various aspects of the study is required before I can recommend the publication of the manuscript.

Please find my comments below:
1.Although historically 67 C is a widely accepted value for Tc of MIT in VO2, Park et al.Nature (2013) paper sets this value to be 65 C. I think this value should be adopted, especially in the context of this paper, as different insulating phases are disregarded.Could the authors either adopt 65 C as Tc or provide reasoning regarding why they use 67 C, which is a relic from old studies on bulk or epitaxial films? 2. Could the authors comment on the presence of M1 and M2 phases in the insulating state of VO2 and how this might affect their conclusions?As they relieved the nonuniform strain due to the substrate adhesion, their crystals should be in either M1 or M2 phase.
3. The authors assumed that hydrogen fraction in VO2 (x) causes a linear change in the Tmit.This is backed up by the ab initio calculations in Ref.19 (in the manuscript) as well as from the gradual shift of the M-I domain wall gradually shift to the other tip when heated towards Tmit^0.However, although samples doped above 100 C for a short duration exhibit such behavior, samples doped at lower temperatures for longer durations show less sharp M-I boundaries, as in Ref. 6.This is also somewhat evident in Figure S6b, as from 2 to 8 to 16 hours the resistance change doesn't seem to follow a sharp boundary.Could the authors explain how this faint M-I boundary fits into the thermodynamic picture they propose?4.Although W-doped measurements somewhat serve that purpose, could the authors elaborate more on the spillover rate of the Pd catalyst at low temperatures, i.e. below Tc?
One peculiar aspect related to the spillover rate is much long durations required for hydrogen doping of W-doped VO2 as compared to the undoped case above Tc.This brings up the issue that if the Pd spillover is slower at lower temperatures along with the lower diffusion coefficient of the insulating phases, there should be an additional correction to the calculated γ factor.5. Relevant to point 4, in Note S4, the authors mention how electrical measurements on tungsten-doped polycrystalline samples are used to measure the diffusion depth.However, no conductivity data is presented.It would be helpful to include the conductivity results in the supporting information.
6.A scale bar to the OM inset of Fig2b would be helpful.

Responses to referees:
Reviewer #1: The present manuscript reports anomalously high energy barrier for dopant diffusion in coexisting phases across the metal to insulator transition point of VO2, and attributed this behavior to the volumetric energy penalty that the diffusers need to pay for the reduction of latent heat.In general, the manuscript is well written and the conclusion is rather interesting.Nevertheless, I have the following suggestions for further improvements.
Thank you for your encouraging and constructive comments!Comment #1: Figure 1c, how the error bar was determined when calculating D?
Response #1: In Fig. 1(c), following ln = ln ( M 2 /), the error bar is determined mathematically: ∆(ln) = ∆/ = 2 M ∆ M /, and ∆ M comes from the measurement of  M .Details of determining ∆ M and ∆(ln) have been added as Note S2 in the supplementary information.
Comment #2: Also for Figure 1c, another thing is that it seems that D is smaller at the insulating phase region approaching to the critical temperature but the D-T tendency seems smooth in the region associated with the metallic phase approaching to the critical temperature.I was wondering how the critical temperature ( MIT ) should be determined, since it is hard to tell whether the metallic and insulating phase 'should' co-exist in across  MIT or just at the temperature region slightly below  MIT ?This needs to be further clarified.
Response #2: This is an insightful comment and points out the uniqueness and complexity of this system: (1)  MIT 0 of the samples is determined to be sharp at 67℃ by optical inspection before any hydrogen treatment.It's mentioned on page 5 of the main text and shown in Fig. S3(b).The dashed line in Fig. 1(c) corresponds to  =  MIT 0 .(2) The M and I phases coexist as long as  anneal <  MIT 0 , not only in the region slightly below  MIT 0 , which has been proved in Fig. S4 ( anneal ≪  MIT 0 ).The offset of  MIT 0 and the kink of the D-T curve is explained in the Supplementary information and summarized here.As shown in Fig. 1(b) and also below, when  anneal is below but close to  MIT 0 , the threshold hydrogen fraction for making the MIT is  MIT ~ 0, hence nearly the entire beam will be in M phase, so the measured D will follow the metallic D-T curve.On the contrary, if  anneal is much lower than  MIT 0 ,  MIT is much higher (approaching  MIT 0 ), the hydrogen diffusion will slow down at the M-I phase boundary, the overall D then follows the insulating D-T curve.
This conclusion has been mentioned on page 9 of main text and proved by the simulations in Fig. S11(b).The captions of Fig. S11(b) have been modified to clarify.
Comment #3: The experiments as demonstrated in Figure 2 was well designed, and in the present case the hydrogenation seems to reduce the resistivity of VO2 that stabilizes the metallic phase.Nevertheless, the hydrogenation of VO2 can also trigger an insulating state under mild hydrogenation temperatures and high hydrogen concentration (e.g., Nat. Mater.2016, 15, 1113, or J. Phys. Chem. Lett. 2022,13,8078), in which situation higher amount of hydrogen will be incorporated within the material.I was wondering whether the mixing phase adjacent to the metal to insulator transition temperature will affect D in this case.
Response #3: In our case of hydrogen diffusion in single-crystalline VO2 microbeams, high concentration (high-H) insulating state (HVO2) has been ruled out by a few experimental evidence: (1) If there was a high-H insulating phase, it should appear at the tip area of microbeams (where H fraction is the highest), and easily differentiated with the metallic phase under optical microscope (Sci.Adv. 2019;5: eaav6815).This should result in an I-M-I domain distribution.However, it has never been observed in our experiment, from 37℃ to 120℃.(2) The lattice expansion of our hydrogen doped VO2 is ~4% (by TEM), much smaller than the reported values for the high-H insulating phase (~10% in Nat.Mater.2016, 15, 1113, or J. Phys. Chem. Lett. 2022,13,8078).This confirms our lower H doping concentrations in the case of VO2 microbeams.
(3) The high-H insulating phase was found in VO2 thin films where the thickness (diffusion path) is on the nanometer scale.For VO2 beams in our case, the diffusion is along the beam direction where the length of diffusion path is over micrometers or longer scale.It will take much longer time (or higher temperature) for hydrogen to reach the end of the diffusion channel (~√) to get saturated -only after that, diffusing hydrogen ions will begin to build up toward the ~ 10% concentration level.Therefore, we do not enter that high-H scenario.
Comment #4: It seems that the less effective hydrogen diffusion within the mixing phase region was caused by the additional energy as caused by the metallicity of VO2 via hydrogenation.Nevertheless, I doubt whether such energy should be considered to be analogous to the latent heat as released when varying temperature across  MIT .Of course this may be correct, but I suggest to be more careful in making a universal conclusion from that perspective.
Response #4: We use the analogy to make the effect more easily understandable to readers, as when the phase transition is triggered by increasing generalized "force": temperature, force, or chemical doping, the corresponding generalized "work" is latent heat, work, or chemical energy.We understand the reviewers' concern due to the abstractness of chemical energy, but from basic thermodynamics we believe it is a good analogy considering the consistency between the analogy and DFT calculations as well as experiments.Nevertheless, we treated the reviewer's comment seriously and modified our wording on page 4 in the main text.
Comment #5: Comparable results to Figure 1c should be also demonstrated for W doped VO2, in which situation the magnitude of TMIT is reduced via substituting V by transition metal with higher valance.Whether this can shift the dash line as shown in Figure 1c leftwards will to some extent testify the universality of the present conclusion.
Response #5: As the reviewer suggests, results on hydrogen diffusion in W-doped VO2 may exclude other factors and make the conclusion universal if the dashed line and the data points would move rightwards (toward lower T).That was exactly why we have performed experiments to compare hydrogen diffusivity in VO2 and W-doped VO2 (Fig. 4(a) and Fig. S13(a)).
To test this and rule out unwanted influence of tungsten in H diffusion (other than simply shifting TMIT) in analysis in Fig. 4(a), we have added an experiment (Fig. S12(a)) to qualitatively compare the hydrogen diffusivity in VO2 and W-doped VO2 at 90℃, a temperature when both are metallic.As shown below in (a), the diffusion rate of hydrogen in M-VO2 and M-W0.015V0.985O2at the same, high temperature is similar to each other.However, in (b), the diffusion is retarded (orders of magnitude) in I-VO2 compared to M-W0.015V0.985O2at the same, low temperature (37℃).Therefore, it is the phase being M or I that causes the diffusion retardation.The retarded diffusivity in VO2 compared with W0.015V0.985O2indicates that the curve in Fig. 1(c) indeed would shift rightwards for W0.015V0.985O2compared to VO2.A related statement has been added to the main text (in front of 'By performing XPS' on page 10 of the main text).
Comment #6: One confirming experiment worthy to be consider in the future (not necessarily to be done now for this work) is associated with the hydrogen diffusion within rare-earth nickelates.From the one side the latent heat across TMIT is much smaller compared to VO2, while the hydrogenation triggered reduction in G should be comparable.From the other side, the resistivity of rare-earth nickelates elevate abruptly, the tendency of which is just the opposite compared to the present one.This will be a perfect supplementary experiment to the present work.
Response #6: Thank you for the suggestion: this comment addresses the universality of this effect in the field of material science, aligning well with what we have proposed in the discussion session.Considering the MIT of rare-earth nickelates as well as the hydrogen induced phase transition induced by d-band electron correlation, a similar effect may exist when hydrogen diffuses within rare-earth nickelates.
However, as the reviewer suggests, rare-earth nickelates turn into a more insulating state (e.g.SmNiO3, Nature Communications 5, 4860 ( 2014)) with hydrogen doping, opposite to the VO2 system.A short discussion and a few references related to this topic has been added into the main text (Discussion Section), and we'll consider doing the experiment in the future.

Reviewer #2:
In this work, the authors provided the effect of second derivative of Gibbs free energy on hydrogen diffusion in VO2.It reported hydrogen faced three times higher energy barrier and over one order of magnitude lower diffusivity when crossing a metal-insulator domain wall in VO2.Furthermore, they employed the first-principles calculations to reveal the hydrogen diffusion along various axes.However, after a comprehensive evaluation of this work, I think it can't provide profound scientific meaning, also can't attract broad attention.
Thank you for your comments!We believe we fully addressed your two comments below.
Comment #1: As shown in Formula (1), it seems that the Gibbs free energy is linear with the hydrogen atomic fraction (x).However, the doping of hydrogen in VO2 could induce a metallic or insulator state depending on the concentration of hydrogen (Nat. Mater.15, 1113, 2016).Obviously, the provided module can't illustrate the effect of high concentration hydrogen on VO2.
Response #1: This comment is similar to the Comment #3 from Reviewer #1.Unlike in VO2 thin films, in hydrogen diffusion along the axial direction of our single-crystalline VO2 microbeams, the high concentration (high-H) insulating state of VO2 (HVO2) does not occur: (4) If there was a high-H insulating phase, it should appear at the tip area of microbeams (where H fraction is the highest), and easily differentiated with the metallic phase under optical microscope (Sci. Adv. 2019;5: eaav6815).This should result in an I-M-I domain distribution.However, it has never been observed in our experiment, from 37℃ to 120℃.(5) The lattice expansion of our hydrogen doped VO2 is ~4% (by TEM), much smaller than the reported values for the high-H insulating phase (~10% in Nat.Mater.2016, 15, 1113, or J. Phys. Chem. Lett. 2022,13,8078).This confirms our lower H doping concentrations in the case of VO2 microbeams.(6) The high-H insulating phase was found in VO2 thin films where the thickness (diffusion path) is on the nanometers or sub-micron scale.For VO2 beams in our case, the diffusion is along the beam direction where the length of diffusion path is over many micrometers or longer scale.It will take much longer time (or much higher temperature) for hydrogen to reach the end of the diffusion channel (~√) to get saturated -only after that, diffusing hydrogen ions will begin to build up toward the ~ 10% concentration level.Therefore, we do not enter that high-H scenario.This is simply akin to the fact that rain can easily flood a pond but cannot easily flood a lake.
Therefore, it is safe to consider only insulating VO2 and metallic HxVO2, as we are limited to the small H fraction scenario.
Comment #2: The diffusion energy barriers of hydrogen along various axes of VO2 were calculated, while the specific diffusion routes should be present in Fig. 3.
Response #2: Thanks for the suggestion to improve the quality.The specific diffusion routes have been added to Fig. S10.Below is an example (along [100]I-phase, monoclinic channel).

Reviewer #3 (Remarks to the Author):
In the present manuscript, one chemical analogy was proposed to display the singularity of the second derivatives of Gibbs free energy across first-order phase transitions, leading to an anomalously high energy barrier for dopant diffusion in co-existing phases within the hydrogenated VO2 single crystal microbeams and polycrystalline films.This work also applied the chemical susceptibility to analyze other co-existing phase systems.In general the manuscript is interesting but the following concerns must to be addressed: Thank you for your comments!We address your comments one by one below.
Comment #1: The author attempts to introduce the contribution of hydrogen occupancy in the driving force of phase transition and explains the singularity caused by this term.In the first paragraph of page 9 of the manuscript, the author points out: "…leads to a chemical energy penalty of |Δγ| for a hydrogen ion to diffuse from an M-domain into an I-domain.This effect is very similar to the mechanical energy penalty of |σMITΔε|…".However, the chemical energy dependency caused by hydrogen might be essentially considered as the stress effect itself.For materials with phase transition, the local chemical stress caused by doping often exhibits the same effect as macroscopic stress, such as biaxial stress caused by the substrate in nickelates(Matter, 2020, 2, 1) and isotopic doping effects in conductive polymers(J.Chem. Soc., Perkin Transaction2, 1995).In Table .S3, it can be seen that the lattice expansion of the hydrogenated rutile phase and intrinsic rutile phase reaches 4%.Therefore, it is suggested that the author increase the discussion on local chemical pressure to exclude the influence of other factors on the analogy of chemical magnetization.
Response #1: The comment states that the effect of local chemical force might be considered as a stress effect itself.The statement itself is correct.In the VO2 system, external stress (such as substrate-imposed strain) and hydrogen doping (which includes a chemical stress effect) both trigger the phase transition.
(1) External stress is absent for our VO2 microbeams which were dry transferred from the growth substrate to and loosely sitting on a new substrate, as confirmed by the sharp phase transition shown in Fig. S3(b).The absence of external stress in this type of unbent, transferred VO2 beams has been extensively discussed in, for example, Nature Nanotechnology, 4, 732(2009).(2) When the formation energy is calculated, the resultant HxVO2 lattice is found to have expanded.The internal chemical stress is, therefore, already included in the total energy calculation and analysis of H diffusion in VO2 (Phys.Chem. Chem. Phys., 2015, 17, 20998).A few sentences have been added to Note S4 to acknowledge and illustrate this point.
Comment #2: Fig. S7 is not mentioned in the main text.The accompanying issue is that this article lacks a sufficient explanation of the structural information, morphology, and orientation of synthesized microbeams in the main manuscript.
Response #2: We apologize for missing this information.Response #3: Hollow triangles and solid circles are data points from two independent samples with the same treatment to prove the repeatability of our measurements.Detailed information has now been added to the captions.
Comment #4: The ex-situ observation of Raman spectra and fitting of diffusion coefficients for hydrogen-induced MIT may overlook some potential factors, such as the chemical gradient introduced by the non-uniform distribution of hydrogen atoms along the microbeams.The influence of this part on the hydrogen diffusion coefficient is usually not significant.But when more hydrogen atoms are pinned onto the domain wall (due to the diffusion barriers, in the author's context), the blocking effect of this part of the chemical gradient is not considered.I suggest the author to further discuss to clarify the effects of enthalpy and formation energy.
Response #4: We suppose that the reviewer is talking about potential high hydrogen concentration pile-up at the domain wall as shown below.A localized high concentration is associated with a localized dip of potential (formation energy), which might be possible at the domain wall.
We did Monte-Carlo simulation to test whether the "pinning" or pile-up of hydrogen atoms will affect the overall diffusion kinetics.According to the simulation below (vertical direction is hydrogen concentration in a.u., horizontal direction is distance along the diffusion direction), the localized hydrogen concentration pile-up is found to be related to the potential dip as  =  0 exp(−∆/k), consistent with Boltzmann distribution.However, the existence of the dip and pile-up at the domain wall does not affect the overall diffusion of ions: curves with different ∆ values collapse onto each other in regions outside the dip region.
In conclusion, even if the hydrogen ions pile up at the M-I domain walls, they won't significantly affect the overall diffusion kinetics, hence our conclusion still holds.However, this analysis does not rule out the hydrogen pinning effect itself; indeed, the domain boundary is an interesting entity worth further investigation as a separate project.We appreciate the reviewer's comment on this!We have added a statement in the main text to address this at the end of discussion of Fig. 4.
Comment #5: In XPS analysis, the integrated area of the peak may be more convincing than the peak intensity.This can be achieved through more detailed peak fitting.
Response #5: This comment is useful to improve the details.The multi-peak fitting is added to Fig. S12.The area info is included in the captions of Fig. S12.
Comment #6: Lack of discussion on the difference in hydrogen diffusion rates between pristine tungsten-doped samples and pristine VO2 samples.The effect of tungsten dopant on hydrogen diffusion may affect the independence of domain wall analysis.
Response #6: This is similar to Comment #5 of Reviewer #1.To rule out the influence of tungsten, we have added the experiment (Fig. S12(a)) to qualitatively compare hydrogen diffusivity in VO2 and W-doped VO2 at 90℃, a temperature when both are metallic phase.In Fig. S12(a), as the reviewer suggests, the multi-peak fitting shows that the diffusion rate of hydrogen in M-VO2 and M-W0.015V0.985O2at the same high temperature is close to each other.However, the diffusion is much retarded (by orders of magnitude) in I-VO2 compared to M-W0.015V0.985O2at a low temperature (37℃).Therefore, it is the phase being M or I that causes the diffusion retardation, not the tungsten dopants themselves.To clarify this, text has been added to the main manuscript (in front of 'By performing XPS' on page 10 of main text).Fig. S12 as shown below is also added into the Supplementary Information.
Comment #7: The analysis of Fig. 1(d) appears in multiple places in the text, which is relatively scattered and not conducive to the coherence of the discourse.The relevant paragraphs on page 7 can be integrated with those on page 9.
Response #7: Thanks for the suggestion on the writing; we suppose the reviewer is talking about the analysis of the Arrhenius plot of diffusivity (Fig. 1(c)).We understand that the analysis on these two pages may look duplicated because the numbers are repeated.However, these numbers are obtained under different logic: the paragraph on page 7 talks about the initial analysis, extracting the slope from the plot mathematically (define the problem), while the paragraph in page 9 talks about the values from numerical simulations of diffusion based on the presented theory (solve the problem).Therefore, we decide to keep the plots as they are to ensure a good logic flow for the readers to follow.
Comment #8: From a microscopic perspective, will hydrogen atoms continuously cross the M-I domain wall barrier during diffusion?This may be related to whether hydrogen is the sole driving force behind the M-I transition when T<TMIT.The lattice expansion caused by electron doping may drive the local transformation of other I-phases.Therefore, hydrogen may be discontinuous across domain walls.The exploration of this mechanism may require deeper calculations and more powerful characterization techniques in the future.
Response #8: This is a great question!Typically the discontinuity of particles' concentration is associated with a stepped potential (e.g. a barrier) such as 2d electron gas in quantum wells (Phys.Rev. B 54, 10609).
(2) If there was a large discontinuity at the domain boundary at Tanneal, while cooling down the microbeams to room temperature, the domain boundary should remain nearly the same location, because the threshold concentration doesn't vary drastically (e.g.,  MIT (41℃)~0.5MIT (20℃)).In contrast, when the microbeam annealed at 41℃ is cooled down to room temperature (optical images shown below), the domain boundary gradually moves toward the high-concentration, left-hand side, showing gradual variation of hydrogen concentration (x) along the diffusion path; therefore, there is no strong discontinuity in x along the beam direction.
As the reviewer suggests, to resolve possible hydrogen concentration discontinuity at these scales in the future, more power techniques may be used, such as nano-SIMS (Annu.Rev. Anal.Chem.2020.13:273-92).
Comment #9: I am curious about the result of simultaneous hydrogenation on both sides of a finite beam.For a sufficiently uniform microbeam, hydrogen is expected to symmetrically promote the formation of the M-phase under the same conditions.When the domain walls on both sides are very close, the phase transition behavior of the central I phase may become anomalous.When any hydrogen atom overcomes a chemical barrier, it will cause a sudden collapse of the domain wall on one side of the phase.This may trigger novel physical phenomena.In future work, the author can continue to explore in depth.
Response #9: This comment provides a future direction for discovering novel phenomena in the present system as a useful material platform.We appreciate the reviewer's suggestion!This further highlights the importance and broad impact of our work for future studies.
Figure S7 (SEM and EBSD) includes the structural info and morphology of the microbeams.The reason why it was not mentioned in the previous version of main manuscript is that the structural info is not the focus of this work; it is included in Fig.S7 for completion purpose.The fact that VO2 prefers to grow along [001]Rutile ([100]Monoclinic) with facets of [110]Rutile ([122]Monoclinic) has been reported in earlier work (e.g., Applied Physics Letters 100, 103111 (2012)).The main text in page 7 is now revised to connect the main text and the supplementary information.Comment #3: Fig.2(b) lacks of detailed legend to distinguish between hollow triangles and solid circles.